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Zapiski Nauchnykh Seminarov POMI, 2015, Volume 436, Pages 174–188 (Mi znsl6166)  
This article is cited in 3 scientific papers (total in 3 papers)

A higher-order asymptotic expansion of the Krawtchouk polynomials

A. R. Minabutdinov

National Research University "Higher School of Economics", St. Petersburg Branch, St. Petersburg, Russia
Full-text PDF (240 kB) Citations (3)
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Abstract: The paper extends the classical result on the convergence of Krawtchouk polynomials to Hermite polynomials. We provide a uniform asymptotic expansion of Krawtchouk polynomials in terms of Hermite polynomials and obtain explicit expressions for a few first terms of this expansion. The research is motivated by the study of ergodic sums of the Pascal adic transformation.
Key words and phrases: Krawtchouk polynomials, asymptotic expansions.
Funding agency Grant number
Russian Foundation for Basic Research 14-01-00373
Received: 21.09.2015
English version:
Journal of Mathematical Sciences (New York), 2016, Volume 215, Issue 6, Pages 738–747
DOI: https://doi.org/10.1007/s10958-016-2879-x
Bibliographic databases:
Document Type: Article
UDC: 517.587+519.214.4
Language: Russian
Citation: A. R. Minabutdinov, “A higher-order asymptotic expansion of the Krawtchouk polynomials”, Representation theory, dynamical systems, combinatorial methods. Part XXV, Zap. Nauchn. Sem. POMI, 436, POMI, St. Petersburg, 2015, 174–188; J. Math. Sci. (N. Y.), 215:6 (2016), 738–747
Citation in format AMSBIB
\Bibitem{Min15}
\by A.~R.~Minabutdinov
\paper A higher-order asymptotic expansion of the Krawtchouk polynomials
\inbook Representation theory, dynamical systems, combinatorial methods. Part~XXV
\serial Zap. Nauchn. Sem. POMI
\yr 2015
\vol 436
\pages 174--188
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6166}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3498192}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2016
\vol 215
\issue 6
\pages 738--747
\crossref{https://doi.org/10.1007/s10958-016-2879-x}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84966587880}
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  • https://www.mathnet.ru/eng/znsl/v436/p174
    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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